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Simulation as a tool for resource management
Conference Paper · February 2000
DOI: 10.1109/WSC.2000.899184 · Source: IEEE Xplore
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Tarek Zayed
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The Hong Kong Polytechnic University
Purdue University
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Proceedings of the 2000 Winter Simulation Conference
J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, eds.
SIMULATION AS A TOOL FOR RESOURCE MANAGEMENT
Tarek M. Zayed
Daniel W. Halpin
Division of Construction Engineering And Management
School of Civil Engineering, Purdue University
West Lafayette, IN 47907-1294, U.S.A.
Due to the complex interaction among units on the
construction job site and in the construction environment,
mathematical models (e.g. queuing systems) can be applied
to only a limited number of special cases. Output from one
operation tends to be the input to the following operation in
construction. This leads to the development of chains of
work tasks as well as situations in which many units are
delayed at processors pending arrival of a required
resource. Such chained or linked situations are too complex
to be modeled using classical queuing models. Simulation
techniques offer the only general methodology that affords
a means of modeling such situations.
One class of simulation models that has been used to
model chains of queues in which units interact is referred
to as the “link-node” modeling format (Teicholz, 1963).
The link-node method gets its name from the chain like or
linked appearance of the graphical representation of the
model. Nodes are located at the end of each link and
indicate an activity.
Simulation techniques can be applied to the modeling
of concrete batch plant operations in order to study different combinations of resources. Micro CYCLONE modeling and programming techniques can be used to simulate
this process. The elements of Micro CYCLONE, originally
developed by Halpin (1973), are used to model and simulate concrete batch plant operations. The Micro
CYCLONE elements used for construction modeling are
shown in Figure 1 (Halpin 1992). Micro CYCLONE is a
simple and powerful tool for construction process
planning, as demonstrated by many researchers.
ABSTRACT
The decision-making process is a very essential part of any
construction operation. Simulation can be used as a tool to
assist construction managers in making informed decisions.
In this paper, simulation is applied to a Concrete Batch
Plant to analyze alternative solutions and resource management. Data is collected to define activity durations for the
plant. A simulation model is constructed for the plant using
the Micro CYCLONE simulation system. Based on sensitivity analysis, management tools are constructed to help the
decision-maker. These tools are a Time-Cost-Quantity
chart, a feasible region analysis and a contour lines chart.
Time-Cost-Quantity and contour lines charts are used for
deciding production time, production cost and required
resources for a required distance from the plant. The
feasible region chart is used for deciding the range of
alternative solutions that can be taken to minimize production time and cost of the available plant resources according to the required transportation distance.
1
INTRODUCTION
A model is a representation of a real-world situation and
provides a framework within which a given situation can
be investigated and analyzed. Models contain and reflect
data that, when interpreted according to certain rules or
conventions, provide information which supports the decision making process. The precision with which these
models reflect the real world varies widely. Abstract or
conceptual models depend on a set of modeling and
interpretive rules. Scheduling networks and bar charts, for
example, have their own individual modeling and interpretive rules. Schematic models are representations that
portray a physical situation (e.g. a map) so that a representational modeling or perception of the real world situation
is achieved. Construction drawings are an excellent
example of a schematic model. Models of various types are
at the heart of problem solving.
2
ANALYSIS OF CONCRETE SUPPLY
This paper develops a simulation approach for the study of
concrete batch plant operations. The results of the study
provide a means of predicting systems production and
defining optimum supply areas around a concrete batch
plant. The optimum areas support efficient resource allocation with minimum duration and cost for different
distances.
1897
Zayed and Halpin
Name
Symbol
Function
This element is always preceded by Queue Nodes.
Before it can commence, units must be available at each
of the preceding Queue Nodes. If units are available,
they are combined and processed through the activity. If
units are available at some but not all of the preceding
Queue Nodes, these units are delayed until the condition
for combination is met.
Combination (COMBI)
Activity
This is an activity similar to the COMBI. However, units
arriving at this element begin processing immediately
and are not delayed.
Normal Activity
This element precedes all COMBI activities and provides a
location at which units are delayed pending combination.
Delay statistics are measured at this element.
Queue Node
It is inserted into the model to perform special
functions such as counting, consolidation, marking,
and statistic collection.
Function Node
It is used to define the number of times of the
system cycles.
Accumulator
Indicates the logical structure of the model and
direction of entity flow.
Arc
Figure 1: Basic CYCLONE Modeling Elements
tower, two belt conveyors, two cement silos, and a discharge unit. This facility serves an area of approximately
15 miles radius. The production capacity of the plant was
rated as approximately 40 cy/hr.
Figure 2 shows the flow diagram for the concrete
batch plant and the transit mixer cycles. The material is
withdrawn from the storage area to fill the batch hopper
through conveyor belt 1. There is a scale for measuring the
aggregate weight in the hopper tower before discharging to
the transit mixer through the conveyor belt 2.
The sub-objectives of this study are as follows:
1- Study of each component of the batch-truck-pump
cycles.
2- Development of a Micro CYCLONE model for
these processes.
3- Collection of data about the duration of each
activity to estimate both deterministic and random
times intrinsic to the model.
4- Simulation of the performance and productivity for
various numbers of trucks and various distances.
5- Calculation of the optimum number of trucks
corresponding to the various distances.
6- Construction of the contour lines for the optimum
travel areas around the batch plant.
7- Development of decision-making tools for
concrete batch plant management to decide the
optimum resource combination with minimum
production time and cost.
3
4
MODEL DESCRIPTION
The model developed consists of several cycles for the
following resources as indicated in Figure 3:
(1) Conveyor 1 is used to transport the aggregates
from the storage area to the storage hopper. It has
three different operations, namely, waiting for the
aggregates, transporting the aggregates, and
maintenance.
(2) A hopper is used for storing the different types of
aggregates. It receives the aggregates from conveyor 1 and stores them for feeding to conveyor 2.
After feeding conveyor 2, it waits for Conveyor 1
to provide re-supply.
MODELING CONTEXT
In order to address the decision-making environment, a
batch plant transit mix delivery operation located in
Lafayette, Indiana was studied. The observed facility
consisted of storage bins for sand and gravel, a hopper
1898
Zayed and Halpin
Cement
Silo
Batch
Hopper
Transit Mixer
Return to Reload
Conveyor 2
Concrete Batch
Plant Storage Area
Delivery
Conveyor 1
Transit Mixer
Loading
Placement
Site
Transit Mixer
Unloading
Transit Mixer
Travel to Site
Pump
Figure 2: Flow Diagram for the Concrete Batch Plant and the Transmit Mixer
1
12
14
0.05
24
7
4
0.90
0.10
8
Hopper
5
42
31
41
28
0.93
10
Conveyor 1
40
Truck Mixer
Conveyor 2
29
0.95
45
27
3
6
43
36
9
0.07
46
Pump
33
34
0.85
37
35
38
47
0.15
11
49
51
60
50
39
Spread
48
43. Truck Available Under Plant
1. Cement Available
11. Truck Maintenance
34. Truck Waiting
3. Hopper Empty
12. Truck Maintenance (2)
35. Move Truck to Pump
4. Feed Hopper
14. Admixture Available
24. Water Available
36. Space Available
27. Load Available
28. Conveyer Available
38. Unload Truck into Pump
39. Pump Available
8. Dummy One
29. Transport Load
40. Truck Returning to Pump
50. Spread & Finish Concrete
9. Dummy Two
31. Load Truck
41. Plant Available
60. Counter
10. Maintenance
33. Travel to Site
42. Truck Moving to Plant
51. End
5. Hopper Occupied
6. Conveyer Available
7. Maintenance
37. Truck Ready to Unload
45. Truck Available
46. Truck Departure
47. Pump Remaining Concrete
48. Concrete Available
49. Crew Available
Figure 3: Micro CYCLONE Schematic Model for Concrete Batching Plant
1899
Zayed and Halpin
(3) Conveyor 2 transports the aggregates from the
hopper to the truck mixer. It waits for the truck
mixer. Following truck loading, maintenance is
done 7%of the time. After feeding the truck
mixer, it waits for the hopper to be available.
(4) The truck mixer transports the concrete from the
plant to the placement sites. To load the truck
mixer, cement, aggregates, water, admixtures, and
conveyor 2 should be available. After the truck
mixer is loaded, it travels to the site where there is
a 15% probability maintenance will be done while
waiting for the pump. To deliver the concrete to
the pump, a truck mixer and a space should be
available beside the pump. After unloading, the
truck mixer returns back to the plant. There is a
5% probability that maintenance will be done
prior to returning to the plant for reload.
(5) The pump receives the concrete from the truck
and supplies it into the pump pipes to the placement sites. After this operation, the pump waits
for other truck mixers to deliver concrete.
(6) Laborers in the placement sites where the concrete
is received from the pump pipes do the spreading
operation. After finishing the spreading operations, labor crews finish the concrete surface.
(7) These tasks are done repetitively.
5
c-
Visual or graphical tests:
- Scatter plot indicates that the straight line
is a good fit for the data.
- Normality assumption for the residual is
achieved and approximately good.
- Constancy assumption for the residual is
approximately good.
- Independence assumption for the residual
is approximately good.
d- Adequacy of the model:
Lack of fit (LOF) test is done for this data
where there are replications in this data. The
probability of LOF-test is p = 0.203 that
indicates that the model is adequate for this
data.
(2) The Return Time was also calculated by regression between Return time and distance: The
model is:
Returning Time(min) = -0.019+1.4003*Distance
(miles).
(Note: pushing the intercept to be zero resulted in
insignificant model.)
Statistical Analysis:
a- Test the Linear Relation:
F-value = 178.64 with probability p = 0.0001.
Then, β1 is O.K. at 5% level of significance
and there is a linear relation between hauling
time and distance.
b- Relative Variation:
r-square = 0.934 where, this is an indicator
that the reduction in variation is small.
c- Visual or graphical tests:
- Scatter plot indicates that the straight line
is a good fit for the data.
- Normality assumption for the residual is
achieved and approximately good.
- Constancy assumption for the residual is
approximately good.
- Independence assumption for the residual
is approximately good.
d- Adequacy of the model:
Lack of fit (LOF) test is done for this data
where there are replications in the data. The
probability of LOF-test is p = 0.1876 that
indicates that the model is adequate for this
data.
(3) Loading and Unloading times are calculated as
BETA distributions from collected data by using a
Beta curve-fitting program.
(4) Other times were estimated as deterministic or
triangular distributions by the plant manager.
DURATION OF SIMULATION ACTIVITIES
In order to build a management decision making tool, data
were collected for the duration that were required for simulating the truck cycle, (i.e. loading, unloading, hauling,
returning, and delay times for truck mixer). In addition,
transport times for sand and gravel and other concrete
ingredients in the batch plant were also required.
(1) The Haul Time was calculated by conducting a
regression analysis relating time and distance for
various distances: The regression model is:
HaulingTime(min) = 0.0571+1.6006*Distance
(miles)
(Note: pushing the intercept to be zero resulted in
insignificant model.)
Statistical Analysis:
a- Test the Linear Relation:
F-value = 259.06 with probability p = 0.0001.
Then, β1 is O.K. at the 5% level of significance and there is a linear relation between
hauling time and distance.
b- Relative Variation:
r-square = 0.9511 where, this is an indicator
that the reduction in variation is small.
1900
Zayed and Halpin
selected as the feasible region of solutions. The same trend
means that a solution should have cost and productivity
that are more than the previous solution to keep it in the
feasible region. Therefore, when a solution combination of
cost and productivity is more than that of the previous
solution, it can not be eliminated since we do not know if it
is feasible or not.
(5) Others are estimated as BETA distributions using
the VIBES Program (Abourizk, 1991).
6
RESOURCES COST ESTIMATION
Cost estimation for the resources that were critical to the
models presented was used to conduct sensitivity analysis
by using different resource combinations. The costs that
are estimated are as follows.
8.1 Selecting Feasible Solutions
The criteria for eliminating infeasible solutions are shown
graphically in Figure 4. In this figure, the cost and productivity combinations are drawn for different sensitivity
analysis results of the simulation model for 5 miles distance. The points provide examples of the resulting sensitivity analysis solutions. Each solution or point has a value
for the productivity and a value for the cost per concrete
cubic yard. The bold lines represent the connection between the cost value and the productivity value for the
feasible solutions and the thin lines represent the connection between the cost value and the productivity value for
the infeasible solutions (e.g. negative cost-productivity
slope). For example, point 1 (solution 1) has a lower cost
than point 2 (solution 2) where it has a higher productivity
than the same point. This means point 1 is more feasible
than point 2. This also means that any solution line (with a
negative slope) intersecting the solution line representing
point 1 could be logically eliminated because it has a
higher cost and lower productivity than point 1. Therefore,
points 2, 9, 10, and 11 are eliminated because of point 1.
Point 8 is eliminated because of point 7 where it has the
same productivity and larger in cost. Point 3 is eliminated
due to point 4 where they are equal in productivity and
point 4 is less in cost. On the other hand, points 1, 4, 5, 6,
and 7 could not be eliminated because the solution lines do
not intersect. In other words, each solution has a higher
cost and a higher productivity than the previous one.
Therefore, one point can not eliminate the other. These
solutions are feasible and the best solution is one of them.
The best solution may not be the lowest cost solution. The
same procedure of selecting the feasible solutions is
followed for the sensitivity results for all the assigned
distances. These sets of solutions corresponding to
different distances are indicated in Figure 5.
Truck cost is estimated as $150 /hr.
Conveyor Belt (1) cost is estimated as $70 /hr.
Conveyor Belt (2) cost is estimated as $ 40 /hr.
Sand & Gravel Hopper cost is estimated as $30 /hr.
7
SIMULATION SENSITIVITY ANALYSIS
Sensitivity analysis was done for the model by varying
different resources. The selected resources were those that
had zero or close to zero percent idleness. This percent
means that these resources are critical in a sense that they
control the process. Therefore, changing them may affect
the production and cost of the operation. The resources
were varied in the model as follows:
•
•
•
•
•
•
•
•
# of trucks: 3 - 5
# of pumping spaces: 1 - 2
# of conveyor (1): 1 - 2
# of conveyor (2): 1 - 2
# of hopper loads: 4 - 5
# of combination is 232 combination.
hauling and returning distance was incremented
by 2 miles starting from 3 mile to 15 miles.
1000 cycles were simulated using the Micro
CYCLONE program.
Simulation was done to analyze the batch plant operation
by investigating these resource combinations and distances
in the model. This analysis is discussed in the following
sections.
8
SIMULATION RESULTS ANALYSIS
Micro CYCLONE was used to simulate the model with
various resource combinations as noted above. Micro
CYCLONE provides a sensitivity analysis report that
includes the productivity and unit cost for each resource
combination or alternative. This report is done for each
distance starting from 3 miles and incremented by two up
to 15 miles. This generates 232 alternative solutions. These
solutions were analyzed to eliminate infeasible solutions.
Sensitivity results were analyzed to eliminate the solutions
that have high cost and low productivity. After this screening, the set of solutions that had the same trend in cost and
productivity (e.g. low cost and high productivity) was
8.2 The Productivity Unit Cost Chart
Based on the criteria explained in Figure 4, the sets of
feasible solutions according to their unit cost, productivity
and different combination of resources are drawn in Figure
5. In this figure, the productivity is drawn against the unit
cost for each feasible solution. The feasible solutions productivity for each of the distances 3, 5, 7, and 9 miles are
close to each other. On the contrary, the feasible solutions
productivity for each of the distances 11, 13 and 15 miles
1901
Zayed and Halpin
35
34.97
34
33.69
33
Point 1
32
31.17
31.17
30.97
31.07
31
30.25
30
30.25
29.22
28.95 29.06
28.56
29
28
Point 3
Point 4
Point 5
28.71
28.71
28.15
27.51 27.71
27
Point 2
Point 6
Point 7
Point 8
26.64
Point 9
26.11
25.90
26
Point 10
25
Point 11
24
Cost ($/cy)
23.27
Productivity (cy/hr)
Point 1
26.64
28.15
Point 2
Point 3
27.71
28.56
28.15
28.71
Point 4
27.51
28.71
Point 5
29.06
30.97
Point 6
33.69
31.17
Point 7
30.25
31.07
Point 8
34.97
31.17
Point 9
29.22
23.27
Point 10
28.95
25.90
Point 11
30.25
26.11
23
Cost and Productivity
Figure 4: Feasible Solutions Selection Chart
(5212)
31.56
(5212)
(5212)
(5222)
(5222)
(5222)
30.56
29.56
(3212)
(5222)
28.56
27.56
(4212)
(3212)
(9Miles)
(3212)
25.56
(11Miles)
24.56
(13Miles)
23.56
(15Miles)
(3211)
22.56
(3211)
Lower Limit
21.56
(3211)
20.56
(3Miles)
(5Miles)
(7Miles)
(5Miles)
(7Miles)
26.56
19.56
(3Miles)
25.2 28.9 26.6 29.1 33.7
28.6 29.6 33.7 33.9 30.2 32.2
34.3 32.5
34
36
35.7 36.3
29.72 31.19
28.15 30.97 31.17
26.25 30.37 31.13
30.98
(9Miles)
22.49 27.96 30.64
(11Miles)
20.93 26.45 30.3
(13Miles)
23.24 28.94
(15Miles)
Lower Limit 29.72 28.94 28.15 27.39 26.63 26.25 27.44 28.63 26.98 22.49 21.97 21.45 20.93 20.59 19.92 0.00 0.00
Upper Limit 31.56 31.56 31.19 31.18 31.17 31.16 31.15 31.13 31.06 30.97 30.89 30.81 30.65 30.53 30.3 29.94 29.58
Unit Cost ($)
Figure 5: Productivity - Unit Cost Chart
1902
Upper Limit
Zayed and Halpin
are widely spread from 20 to 30 units/hr on average.
However, The best solution may not be the lowest cost
solution because the productivity of the highest cost
solution is approximately 1.5 that of the lowest cost
solution in which the cost is not varied too much.
Figure 5 shows some numbers between brackets that
represent the possible resource combinations. The order of
these resources is # of truck mixers, # of pumping spaces, #
of conveyor 1, and # of conveyor 2 from left to right
respectively. For example, if 3 truck mixers, 2 pump
spaces, 1 conveyor 1, and 2 conveyor 2 are used, then, the
productivity (unit/hr) will be 29.72 for 3 miles distance.
On the other hand the cost will be $25.24 per unit of
production. It also shows the feasible region for each set of
solutions for different distances. This region is limited by
the minimum (lower) and maximum (upper) productivity
limits for each set corresponding to various distances. This
decision region or zone helps the decision-maker to take
his action according to productivity, unit cost, distance and
the combination of resources that is required to achieve this
productivity and cost.
8.3 Use of Contour Lines Chart
Figure 6 indicates the position of the concrete batch plant
under study within the West Lafayette and Lafayette
(Indiana) area. The contour lines represent the different
distances around the batch plant. They represent the surrounding distances 3, 5, 7, 9, 11, 13, 15 miles from the
concrete batch plant within the West Lafayette and
Lafayette area. The lowest cost solution is assigned to each
contour line to indicate the productivity, unit cost and
combination of resources that is feasible for each distance
or contour line. Consequently, the plant management is
capable of deciding the price and time of providing concrete for these various distances if they have any order
within these regions. On the other hand, plant management
could decide the optimum set of resources that could produce the required amount of concrete within these borders.
Figure 6: Contour Lines for Distances, Production
Times and Resources
to deliver the required concrete but this depends on the client
time limits and the availability of the resources. The feasible
region for the decision making process indicates that
management can use other resource combinations.
Based on the lowest cost solution (resource combination), a set of curves is constructed to measure the time and
cost for various concrete quantities to different distances.
Figure 7 indicates this set of curves. In this figure, with a
known concrete quantity, the duration of concrete delivery
can be determined. In addition, the unit cost and the total
cost based on different resource combinations for various
distances can be determined. Suppose that the concrete
batch plant management has a client who is 13 miles from
the plant and requests 100 cy of concrete. Based on the
chart in Figure 6, the management can inform him that the
delivery time will be in approximately 5 hours and cost
$32.49 +overhead + profit per cubic yard. The management will know that it needs 3 truck mixers, 2 pump
spaces, 1 conveyor 1, and 1 conveyor 2 to achieve this
quantity at this delivery time.
8.4 Using the Charts
Consider a case in which a client at the intersection of
state road 26 and state road 52 requests an amount of
concrete. Management must decide the cost, the time, and
the resources needed to deliver the required amount of
concrete. Based on the contour lines chart, this client will be
13 miles from the plant. Figure 4 indicates that the
productivity will be 20.93 units/hr where the unit cost will
be $32.49/unit. It also indicates that the optimum resources
required will be 3 truck mixers, 2 pump spaces, 1 conveyor
1, and 1 conveyor 2 (3211). Based on Figure 5, the management can use other resource combinations, such as (5222)
1903
Zayed and Halpin
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
Unit Cost:
3m: $25.24: 3212
5m: $26.64: 3212
7m: $28.57: 3212
9m: $30.79: 4212
11m: $30.24: 3211
13m: $32.49: 3211
15m: $34.73: 3211
Time(3m)
Time(5m)
Time(7m)
Time(9m)
Time(11m)
Time(13m)
Time(15m)
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
200
Time(3m)
1.01
1.35
1.68
2.02
2.36
2.69
3.03
3.36
3.70
4.04
4.37
4.71
5.05
5.38
5.72
6.06
6.73
Time(5m)
1.07
1.42
1.78
2.13
2.49
2.84
3.20
3.55
3.91
4.26
4.62
4.97
5.33
5.68
6.04
6.39
7.10
Time(7m)
1.14
1.52
1.90
2.29
2.67
3.05
3.43
3.81
4.19
4.57
4.95
5.33
5.71
6.10
6.48
6.86
7.62
Time(9m)
1.03
1.37
1.71
2.05
2.39
2.74
3.08
3.42
3.76
4.11
4.45
4.79
5.13
5.47
5.82
6.16
6.84
Time(11m) 1.33
1.78
2.22
2.67
3.11
3.56
4.00
4.45
4.89
5.34
5.78
6.22
6.67
7.11
7.56
8.00
8.89
Time(13m) 1.43
1.91
2.39
2.87
3.34
3.82
4.30
4.78
5.26
5.73
6.21
6.69
7.17
7.64
8.12
8.60
9.56
Time(15m) 1.53
2.04
2.55
3.06
3.58
4.09
4.60
5.11
5.62
6.13
6.64
7.15
7.66
8.17
8.68
9.19
10.21
Quantity (cy)
Figure 7: Time-Cost-Quantity Chart
The steps for calculating the decision index are as
follow:
8.5 The Best Set of Solutions
In many circumstances, the best solution may not be the
minimum cost solution because this is a multi-objective
problem where productivity and cost both influence the
decision. Therefore, a method for deciding the best
solution from a productivity-cost point of view is applied.
A decision index method is used. This decision index
allows one to distinguish between the different solutions
inside the feasible zone for each distance. This method
relies on the difference between the unit costs of different
solutions and the differences in productivity. In other
words, if a solution has a cost difference that is less than
the productivity difference referenced to the lowest cost
solution, this solution is better than the lowest cost solution
and vice versa. Consequently, the best solution may or may
not be the lowest solution. The following example explains
the procedure of calculating the decision index to select the
best solution in the feasible set for each distance.
1- Divide the unit cost ($/cy) by the productivity
(cy/hr) for each solution of the feasible region.
2- To compare all the feasible solutions to the lowest
cost solution, divide the results of step 1 for all
other candidate solutions by the result of step 1
for the lowest cost solution.
3- The result will be the decision index. The index
for the lowest cost solution is 1.0 since the same
number is divided by itself. If the index for any
solution is less than 1 as in case 2, this means that
this solution is better than the lowest cost solution
because the distribution of the unit cost over the
productivity is less than that of the lowest cost
solution. In case 3, the distribution of the unit cost
over the productivity is greater than that of the
lowest cost solution. Therefore, the solution in
case 3 is not better than the lowest cost solution.
According to this methodology, all the feasible
solutions for each distance are analyzed using the
decision index technique. Table 1 indicates the
decision index for all the feasible solutions.
4- If the decision index is below one for more than
one solution, select the solution of the lowest
index value.
8.5.1 Example
Based on 5 miles distance simulation model results, three
candidate combinations are identified in Table 1.
Table 1: Simulation Results Candidates
Combination
1- (3212)
Cost
$26.64
Produc
-tivity
28.15
2- (4212)
$29.06
30.97
3- (3222)
$27.51
28.71
($/cy)/
(cy/hr)
26.64/28.15
=0.9464
29.06/30.97
=0.9383
27.51/28.71
=0.9582
Index
1.00
Table 2 explains this operation for our simulation model
where the index for each solution is indicated in front of
each case. The lowest cost solution has an index of 1.0. If
the solution index is bigger than 1.0, then this solution is not
more feasible than the lowest cost solution. According to
Table 2, the best solution for distances 3 and 9 miles is the
0.9915 < 1
1.0125 > 1
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Zayed and Halpin
Table 2: Decision Index Calculation for the Simulation Model
Combination
Cost ($/cy)
(3Miles)
3212
3222
4212
5212
3212
3222
4212
4222
5212
3212
3222
4212
4222
5212
4212
5212
5222
3211
3221
4212
4222
5212
5222
3211
4212
5212
5222
3211
4211
4212
5212
5222
25.24
26.06
28.86
34.61
26.64
27.51
29.06
30.25
33.69
28.57
29.58
29.63
30.61
33.73
30.79
33.89
35.14
30.24
31.76
32.19
33.2
34.27
35.42
32.49
34.03
35.09
35.97
34.73
35.71
36.14
36.28
37.08
(5Miles)
(7Miles)
Distances
(9Miles)
(miles)
(11Miles)
(13Miles)
(15Miles)
29.72
30.31
31.19
31.2
28.15
28.71
30.97
31.07
31.17
26.25
26.71
30.37
30.71
31.13
29.23
30.98
31.02
22.49
22.67
27.96
28.31
30.64
30.77
20.93
26.45
29.92
30.3
19.58
23.24
24.91
28.94
29.4
Decision
Index
1.0000
1.0124
1.0762
1.1989
1.0000
1.0125
0.9915
1.0288
1.1421
1.0000
1.0175
0.8964
0.9158
0.9955
1.0000
1.0385
1.0754
1.0000
1.0419
0.8562
0.8722
0.8318
0.8561
1.0000
0.8288
0.7555
0.7647
1.0000
0.8663
0.8179
0.7068
0.7111
is a powerful tool for batch plant management, it supports
rapid decision making regarding concrete delivery time,
concrete prices and plant resource combinations.
lowest cost solution. It is different for the other distances
since by increasing a cost slightly, the productivity grows to
be on average 1.5 more than the lowest cost solution.
Therefore, this index is recommended for selection of the
best solution among the feasible solutions or feasible region.
Based on this index, the best solution is the lowest cost
solution for 3 and 9 miles where the resource combinations
are (3212) and (4212) respectively. The best solutions for
the other distances are shown in Table 3.
9
SUMMARY AND CONCLUSION
In conclusion, this paper has discussed the role of simulation as a tool for decision-making and resource management. The concrete batch plant example is presented as a
case study to demonstrate how simulation can be of
benefit.
Simulation sensitivity analysis is used to generate some
useful decision-making tools for plant operation. These tools
are a Time-Cost-Quantity chart, a feasible region for decision-making processes and a contour lines chart. The TimeCost-Quantity and contour lines charts are used for deciding
production time, production cost and required resources for a
required distance from the plant. The Feasible region chart is
used for deciding the range of alternative solutions available
to minimize production time and cost of the available plant
resources according to the required transport distance.
Consequently, simulation sensitivity analysis can be
used as a very powerful tool for decision-makers and
Table 3: The Best Solutions for Different Distances
Resource Combination
Miles
(4212)*
5
(4212) *
7
(5212) *
11
(5212) *
13
(5212) *
15
*Where: the combination (4212) means: 4 truck
mixers, 2 pumping spaces, 1 conveyor #1, and 2
conveyor #2 respectively.
Based on the best solutions that are selected from
Table 1, the Time-Cost-Quantity chart is reconstructed for
the simulation model as indicated in Figure 8. This figure
1905
Zayed and Halpin
7.00
6.75
6.50
6.25
6.00
5.75
5.50
5.25
5.00
4.75
4.50
4.25
4.00
3.75
3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
Unit Cost:
3m: $25.24: 3212
5m: $29.06: 4212
7m: $29.63: 4212
9m: $30.79: 4212
11m: $34.27: 5212
13m: $35.09: 5212
15m: $36.28: 5212
Time(3m)
Time(5m)
Time(7m)
Time(9m)
Time(11m)
Time(13m)
Time(15m)
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
200
Time(3m)
1.01
1.35
1.68
2.02
2.36
2.69
3.03
3.36
3.70
4.04
4.37
4.71
5.05
5.38
5.72
6.06
6.73
Time(5m)
0.97
1.29
1.61
1.94
2.26
2.58
2.91
3.23
3.55
3.87
4.20
4.52
4.84
5.17
5.49
5.81
6.46
Time(7m)
0.99
1.32
1.65
1.98
2.30
2.63
2.96
3.29
3.62
3.95
4.28
4.61
4.94
5.27
5.60
5.93
6.59
Time(9m)
1.03
1.37
1.71
2.05
2.39
2.74
3.08
3.42
3.76
4.11
4.45
4.79
5.13
5.47
5.82
6.16
6.84
Time(11m) 0.98
Time(13m) 1.00
1.31
1.63
1.96
2.28
2.61
2.94
3.26
3.59
3.92
4.24
4.57
4.90
5.22
5.55
5.87
6.53
1.34
1.67
2.01
2.34
2.67
3.01
3.34
3.68
4.01
4.34
4.68
5.01
5.35
5.68
6.02
6.68
Time(15m) 1.04
1.38
1.73
2.07
2.42
2.76
3.11
3.46
3.80
4.15
4.49
4.84
5.18
5.53
5.87
6.22
6.91
Quantity (cy)
Figure 8: Time-Cost-Quantity Chart Based on Best Solution
Teicholz, P. 1963. A simulation approach to the selection
of construction equipment, Technical Report No. 26,
Construction Institute, Stanford University, June.
resource management not only for concrete batch plants
but for any construction operation as well.
REFERENCES
AUTHOR BIOGRAPHIES
Abou Rizk, S. M.; Halpin D. W., and Wilson, V. R. 1991.
Visual interactive fitting of beta distributions, Journal
of Construction Engineering and Management, ASCE,
117(4): 205-215.
American Society of Civil Engineers (ASCE) 1994.
Standard Practice for Concrete for Civil Works
Structures, ASCE Press, New York, PP.57.
Camillo, J. 1996. Controlling the flow of truck mixers,
Concrete Journal, 14(4):250-256.
Halpin, D. W. and Riggs, L. S. 1992. Planning and
analysis of Construction Operations, New York: John
Wiley & Sons.
James E. Russell, 1985. Construction Equipment, Reston,
VA: Reston Publishing Company.
National Concrete Machinery Company 1976. Concrete
Mobile Hand Book, IRL Associates Inc.
National Ready Mixed Concrete Association (NRMCA)
1995. Truck Mixer Driver’s Manual, Publication No.
188, Silver Spring, MD.
Peurifoy, R. L.; Ledbetter, W. B. and Schexnayder, C. J.
1996. Construction Planning, Equipment, and
Methods, 5th Edition, New York: McGraw-Hill.
Strehlow, R. W. 1973. Concrete Plant Production,
National Ready Mixed Concrete Association
(NRMCA), Publication No. 105, Silver Spring, MD.
Strehlow, R. W. 1974. Relating Concrete Plant Production
to Equipment Selection, National Ready Mixed
Concrete Association (NRMCA), Publication No. 145,
Silver Spring, MD.
TAREK M. ZAYED is an Assistant Lecturer in Construction Engineering department at Zagazig University,
Zagazig, EGYPT. He received his B.S. and M.S. degrees in
Construction Engineering and Management from Zagazig
University, EGYPT in 1988 and 1992 respectively. He has
been working toward his Ph.D. in Construction Engineering and Management in the school of Civil Engineering at
Purdue University, West Lafayette, Indiana since 1997. His
M.S. thesis was in studying the production efficiency of
concrete batch plants. His Ph.D. thesis is in the area of
applying artificial intelligence techniques to the construction productivity especially concrete bored piles. His email
address is <zayed@ecn.purdue.edu>.
DANIEL W. HALPIN is Professor and Head of the Division of Construction Engineering and Management at
Purdue University in West Lafayette, Indiana. He received a
B.S. degree from the U.S. Military Academy at West Point
in 1961. He received M.S. and Ph.D. degrees in Civil Engineering from the University of Illinois in Champaign in
1969 and 1973 respectively. He was on the faculty at
Georgia Tech (1973-1985), and held the A. J. Clark Chair
Professor Position at the University of Maryland (19851987). He developed the CYCLONE methodology for construction simulation. He has received many awards, including the Huber and Peurifoy Awards, for his contributions to
computer applications in civil and construction engineering.
His email address is <halpin@ecn.purdue.edu>.
1906
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